The invention disclosed and claimed herein generally pertains to a method and apparatus for computed tomography (CT) cone-beam imaging by means of the Radon transform, wherein x-ray projection data is converted to Radon planar integral data by computing respective Radon derivatives from the projection data.
One of the most important techniques currently used in constructing a CT image of an object is based on the Radon transform. This technique is of particular importance in three-dimensional (3D) CT imaging. According to such technique, a cone-beam x-ray source irradiates the object while traversing a scan path to project an image of the object, in the form of cone-beam x-ray data, onto a detector plane. A two-step process is then performed, wherein the cone-beam data is converted into a set of Radon data, or planar integrals defined in Radon space, and an inverse Radon transform is performed using the planar integrals to construct the image. It is known that this process is most usefully carried out by computing the radial derivative (Radon derivative) for each planar integral in the set, from which the values of respective planar integrals can be readily determined.
Commonly assigned U.S. Pat. No. 5,257,183, issued Oct. 26, 1993 to Kwok C. Tam, the inventor named herein, discloses a very effective technique for computing the Radon derivatives for use in the above process. While this technique works quite well, a great deal of computational effort is required. In the past, this has been achieved by partitioning the Radon space by means of a set of coaxial planes, such as the set of vertical or azimuthal planes shown in FIG. 4 of the above-referenced U.S. Pat. No. 5,257,183. Each of such planes is provided with a coordinate system comprising a set of grid points, organized as a circular polar grid centered at an origin common to all of the planes. The coaxial planes partition the Radon space so that each data point in a Radon data set lies in one or another of the planes, at a grid point thereof. To determine respective derivatives, a number of adjacent azimuthal planes are typically assigned to each processor in an array of processors. Each processor computes the Radon derivatives for the Radon data points lying in its assigned planes. Thus, the processors can be operated in parallel, that is, simultaneously and independently from one another, to reduce time and complexity in determining the derivatives.
Notwithstanding the benefits of the above arrangement, it has been found that for a given view angle, the number of Radon data points lying in respective azimuthal partitioning planes for which derivatives must be computed, can vary extensively from plane to plane. Moreover, as described hereinafter in greater detail, the number of required derivative computations may be very different for different groups of adjacent planes. Accordingly, the processors tend to have very different workloads from one another, if computational tasks are assigned on the prior art basis described above.
It would be highly desirable to assign each processor approximately the same number of derivative computations to perform, for a given view angle. Workloads of the respective processors would then be fairly even, and the processors could be operated with significantly improved efficiency.